This work concerns itself on two new coupled mKdV systems, the first with time-dependent coefficients, and the second with constant coefficients. The soliton ansatz will be used for the first system to obtain 1-bright soliton solution. The simplified form of the bilinear method will be used to derive multiple-soliton solutions and multiple singular soliton solutions for the second coupled mKdV ...

We consider the solution of spectral problems with elliptic potentials in the framework of the Hermite ansatz. We show that the search for potentials and their spectral characteristics is reduced to a system of polynomial equations solvable by the Gröbner bases method and others. New potentials and corresponding solutions of the Sawada–Kotera, Kaup–Kupershmidt, Boussinesq equations are found.

The thermodynamic Bethe ansatz method is employed for the study of the integrable critical RSOS(q1, q2; q) model. The high and low temperature behavior are investigated, and the central charge of the effective conformal field theory is derived. The obtained central charge is expressed as the sum of the central charges of two generalized coset models.

The eigenvalues of the elliptic N-body Ruijsenaars operator are obtained by a dynamical version of the algebraic nested Bethe ansatz method. The result is derived by using the construction given in [1], where the Ruijsenaars operator was obtained as the transfer matrix associated to the symmetric power of the vector representation of the elliptic quantum group Eτ,γ(glN ).

We evaluate typical performance of irregular low-density generator-matrix (LDGM) codes, which is defined by sparse matrices with arbitrary irregular bit degree distribution and arbitrary check degree distribution, for lossy compression. We apply the replica method under one-step replica symmetry breaking (1RSB) ansatz to this problem. Typical performance of irregular LDGM codes for lossy compre...

The basics of the thermodynamic Bethe ansatz equation are given. The simplest case is repulsive delta function bosons, the thermodynamic equation contains only one unknown function. We also treat the XXX model with spin 1/2 and the XXZ model and the XYZ model. This method is very useful for the investigation of the low temperature thermodynamics of solvable systems.

The goal of this paper is to demonstrate a method for tensorizing neural networks based upon an efficient way of approximating scale invariant quantum states, the Multi-scale Entanglement Renormalization Ansatz (MERA). We employ MERA as a replacement for linear layers in a neural network and test this implementation on the CIFAR-10 dataset. The proposed method outperforms factorization using te...

As a prelude to a truly non-perturbative evaluation of the e ective potential in terms of lattice QCD, the one loop e ective potential for a non-Abelian gauge con guration is calculated using the background eld method. Through a non-trivial correlation between the space and color orientations the new background eld avoids the possible coordinate singularity, DetBa i = 0, observed recently by Ke...

We demonstrate that the configuration interaction ~CI! approximation recaptures essential features of the exact ~Bethe-ansatz! solution to the one-dimensional ~1D! Hubbard model. As such, it provides a valuable route for describing effects that go beyond mean-field theory for strongly correlated electron systems in higher dimensions. The CI method systematically describes fluctuation and quantu...

An adaptive variational quantum imaginary time evolution (AVQITE) approach is introduced that yields efficient representations of ground states for interacting Hamiltonians on near-term computers. It based McLachlan's principle applied to wave functions. The parameters evolve deterministically according equations motions minimize the difference exact evolution, which quantified by McLachlan dis...